On Thu, Sep 26, 2002 at 12:46:29PM +0200, Bruno Marchal wrote:
> I would say the difference between animals and humans is that humans
> make drawings on the walls ..., and generally doesn't take their body
> as a limitation of their memory.
It's possible that we will never be able to access more than a
bounded volume of space. It depends on the cosmology of our universe.
> It is also the difference between
> finite automata, and universal computers: those ask always for more
> memory; making clear, imo, the contingent and local character of their
> space and time bounds.
My point is that our inability to compute non-recursive functions is also
a contingent bound. It's contingent on us not discovering a non-recursive
law of physics.
> I have read and appreciate a lot of papers by Shapiro. He has edited
> also the north-holland book "Intensionnal Mathematics" which I find
> much interesting than its "case for Second-order Logic".
> It is not very important because, as you can seen in Boolos 93, basically
> the logic G and G* works also for the second order logic. Only the
> restriction to Sigma_1 sentences should be substituted by a substitution
> to PI^1_1 sentences. This can be use latter for showing the main argument
> in AUDA can still work with considerable weakening of comp, but I think
> this is pedagogically premature.
I guess I'll have to take your word for it.
BTW, you never answered my earlier question of why Arithmetical Realism
rather than Set Theoretic Realism. Is is that you don't need more than
Arithmetical Realism for your conclusions? What do you personally believe?